As an encoding method in which, in a case of performing image (data) encoding, coefficients of sub-bands (frequency bands) generated by performing a band division process on an input image are encoded, there is JPEG (Joint Photographic Experts Group) 2000.
In a case of encoding an image using the JPEG 2000 method, wavelet coefficients obtained by performing wavelet transform on the input image are quantized, and the quantized coefficients obtained through the quantization further undergo entropy encoding.
In the related art, in entropy encoding, bit modeling called EBCOT (Embedded Block Coding with Optimized Truncation) and arithmetical encoding called MQ coder are performed. That is to say, quantized coefficients undergo bit modeling, and further undergo arithmetical encoding based on a plurality of coding paths for each bit plane. The code obtained through the arithmetical encoding is output as an encoded image (data) (for example, refer to JP-A-2004-166254).
In addition, in a case of decoding an image encoded using the JPEG 2000 method, a process is performed with procedures reverse to the case of encoding. More specifically, the code which is the encoded image data undergoes entropy decoding and then is inversely quantized, and the quantized coefficients obtained thereby further undergo inverse wavelet transform. The image obtained by the inverse wavelet transform is output as a decoded image.